IT Fundamentals: Applied Data Science with R, Syllabus
Some Notes on TensorFlow2 and Markov
nvidia-smi will confirm that you have a GPUThis notebook contains the code samples
If you compile to pdf,
Training a neural network revolves around the following objects:
You can visualize their interaction as illustrated in figure 3.1:
Figure 3.1 The network, layers, loss function, and optimizer
A layer is a data-processing module that
Some layers are stateless, but more frequently layers have a state:
Different layers are appropriate for
For instance,
You can think of layers as the LEGO bricks of deep learning,
Building deep-learning models in Keras is done by
The notion of layer compatibility here refers specifically to the fact that
A deep-learning model is a directed, acyclic graph of layers.
Some common ones include the following:
The topology of a network defines a hypothesis space.
Picking the right network architecture
The next few chapters will both teach you
Once the network architecture is defined, you still have to choose two more things:
A neural network that has multiple outputs
Choosing the right objective (or loss) function
Imagine a stupid, omnipotent AI
Fortunately, when it comes to common problems
For instance, the Loss Functions you’ll use are
Only when you’re working on truly new research problems
Going forward we’ll detail explicitly
Keras is a deep-learning framework that
Keras was initially developed for researchers,
Keras has the following key features:
This means Keras is appropriate for building essentially any deep-learning model,
Keras and its R interface
The Keras R package is compatible with R versions 3.2 and higher.
The documentation for the R interface
The main Keras project website
Keras has well over 250,000 users (as of 2018),
Keras is used at Google, Netflix, Uber, CERN, Yelp, Square, and others
Keras is also a popular framework on Kaggle,
Figure 3.2 Google web search interest for different deep-learning frameworks over time
Keras is a model-level library,
It doesn’t handle low-level operations
Currently, the three existing backend implementations are
In the future, it’s likely that Keras will be extended
One popular Deep Learning Framework is PyTorch
You can see mulitple deep learning frameworks here.
Figure 3.3 The deep-learning software and hardware stack
TensorFlow, CNTK (deprecated), and Theano (deprecated)
Starting in 2011, Google Brain built DistBelief
Google has also developed the Tensor Processing Unit
Any piece of code that you write with
Keras
We recommend using the TensorFlow backend
Via TensorFlow (or Theano, or CNTK), Keras is able to run seamlessly
When running on CPU, TensorFlow is itself
On GPU, TensorFlow
You’ve already seen one example of a Keras model:
The typical Keras workflow looks just like that example:
There are two ways to define a model:
As a refresher, here’s a two-layer model
model <- keras_model_sequential() %>%
layer_dense(units = 32, input_shape = c(784)) %>%
layer_dense(units = 10, activation = "softmax")
And here’s the same model defined using the functional API:
input_tensor <- layer_input(shape = c(784))
output_tensor <- input_tensor %>%
layer_dense(units = 32, activation = "relu") %>%
layer_dense(units = 10, activation = "softmax")
model <- keras_model(inputs = input_tensor, outputs = output_tensor)
With the functional API,
Once your model architecture is defined,
The learning process is configured in the compilation step,
Here’s an example with a single loss function,
model %>% compile(
optimizer = optimizer_rmsprop(lr = 0.0001),
loss = "mse", metrics = c("accuracy")
)
Finally, the learning process
model %>% fit(input_tensor, target_tensor, batch_size = 128, epochs = 10)
Going forward we’ll build a solid intuition
In this example, we will learn to classify movie reviews
Lets check that we have TF2 and a GPU setup
tensorflow::as_tensor(1)## tf.Tensor(1.0, shape=(), dtype=float64)
And below, you’ll see active R code blocks
We’ll be working with “IMDB dataset”,
For instance, it is possible that your model
Just like the MNIST dataset,
It has already been preprocessed:
library(keras)
imdb <- dataset_imdb(num_words = 10000)
c(c(train_data, train_labels), c(test_data, test_labels)) %<-% imdb# ```{r}
library(keras)
# imdb <- dataset_imdb(num_words = 10000) # here keras reads it from AWS storage
imdb <-
readRDS("./data/imdb.rds") # or load copy stored in data subfolder
c(c(train_data, train_labels), c(test_data, test_labels)) %<-% imdb
The argument num_words = 10000
The variables train_data and test_data are
lists of reviews,
train_labels and test_labels are lists of
0s and 1s,
str(train_data)## List of 25000
## $ : int [1:218] 1 14 22 16 43 530 973 1622 1385 65 ...
## $ : int [1:189] 1 194 1153 194 8255 78 228 5 6 1463 ...
## $ : int [1:141] 1 14 47 8 30 31 7 4 249 108 ...
## $ : int [1:550] 1 4 2 2 33 2804 4 2040 432 111 ...
## $ : int [1:147] 1 249 1323 7 61 113 10 10 13 1637 ...
## $ : int [1:43] 1 778 128 74 12 630 163 15 4 1766 ...
## $ : int [1:123] 1 6740 365 1234 5 1156 354 11 14 5327 ...
## $ : int [1:562] 1 4 2 716 4 65 7 4 689 4367 ...
## $ : int [1:233] 1 43 188 46 5 566 264 51 6 530 ...
## $ : int [1:130] 1 14 20 47 111 439 3445 19 12 15 ...
## $ : int [1:450] 1 785 189 438 47 110 142 7 6 7475 ...
## $ : int [1:99] 1 54 13 1610 14 20 13 69 55 364 ...
## $ : int [1:117] 1 13 119 954 189 1554 13 92 459 48 ...
## $ : int [1:238] 1 259 37 100 169 1653 1107 11 14 418 ...
## $ : int [1:109] 1 503 20 33 118 481 302 26 184 52 ...
## $ : int [1:129] 1 6 964 437 7 58 43 1402 11 6 ...
## $ : int [1:163] 1 7092 1662 11 4 1749 9 4 2165 4 ...
## $ : int [1:752] 1 33 4 5673 7 4 2 194 2 3089 ...
## $ : int [1:212] 1 13 28 64 69 4 8742 7 319 14 ...
## $ : int [1:177] 1 3432 26 9 6 1220 731 939 44 6 ...
## $ : int [1:129] 1 617 11 3875 17 2 14 966 78 20 ...
## $ : int [1:140] 1 466 49 2036 204 2442 40 4 6724 732 ...
## $ : int [1:256] 1 13 784 886 857 15 135 142 40 2 ...
## $ : int [1:888] 1 4 712 19 2 2 2 963 2 26 ...
## $ : int [1:93] 1 4 204 7610 20 16 93 11 9075 19 ...
## $ : int [1:142] 1 14 9 6 55 641 2854 212 44 6 ...
## $ : int [1:220] 1 4 288 310 3202 7 241 672 4 2 ...
## $ : int [1:193] 1 75 69 8 140 8 35 2 38 75 ...
## $ : int [1:171] 1 4679 2784 1482 11 450 7 134 364 352 ...
## $ : int [1:221] 1 13 28 332 4 274 6 378 7 211 ...
## $ : int [1:174] 1 13 1059 14 33 6 2181 2824 32 13 ...
## $ : int [1:647] 1 6 565 255 5964 875 103 196 167 2 ...
## $ : int [1:233] 1 4 86 390 1241 520 6 52 1384 51 ...
## $ : int [1:162] 1 13 92 124 51 12 9 13 169 38 ...
## $ : int [1:597] 1 111 28 3431 15 2 475 455 4127 9 ...
## $ : int [1:234] 1 1255 1223 5547 1265 2390 1747 8 4 268 ...
## $ : int [1:51] 1 806 13 43 161 169 4 875 551 17 ...
## $ : int [1:336] 1 23 3333 7449 7505 4 254 157 2 7 ...
## $ : int [1:139] 1 17 19 111 85 1719 1181 3135 201 14 ...
## $ : int [1:231] 1 14 38 446 1034 9 394 13 435 8 ...
## $ : int [1:704] 1 14 16 4 840 5582 20 5 4 236 ...
## $ : int [1:142] 1 14 22 16 23 522 33 314 54 13 ...
## $ : int [1:861] 1 1710 14 733 1367 1028 81 24 332 48 ...
## $ : int [1:132] 1 4 229 18 14 248 1844 1422 9 38 ...
## $ : int [1:122] 1 3420 9 34 230 61 514 7 32 7 ...
## $ : int [1:570] 1 11 14 4419 3073 14 9061 50 26 1093 ...
## $ : int [1:55] 1 568 65 9 4689 31 7 4 118 495 ...
## $ : int [1:214] 1 806 21 13 80 2372 199 4 114 347 ...
## $ : int [1:103] 1 54 7850 5397 8633 7455 9 2090 2 23 ...
## $ : int [1:186] 1 13 244 1713 1681 8 97 134 243 7 ...
## $ : int [1:113] 1 13 165 219 14 20 33 6 750 17 ...
## $ : int [1:169] 1 159 13 296 14 22 13 332 6 733 ...
## $ : int [1:469] 1 14 364 1242 2460 2 47 43 77 7548 ...
## $ : int [1:138] 1 1400 168 855 19 12 50 26 76 128 ...
## $ : int [1:302] 1 101 20 11 63 7564 2 46 1421 6 ...
## $ : int [1:766] 1 5011 892 711 12 2774 38 2428 145 11 ...
## $ : int [1:351] 1 1318 13 191 264 146 4 86 5 64 ...
## $ : int [1:146] 1 13 974 13 69 8 702 930 143 14 ...
## $ : int [1:59] 1 13 296 4 20 11 6 4435 5 13 ...
## $ : int [1:206] 1 209 888 14 22 47 8 30 31 7 ...
## $ : int [1:107] 1 13 219 14 33 4 2 22 1413 12 ...
## $ : int [1:152] 1 591 92 851 42 60 104 44 2644 14 ...
## $ : int [1:186] 1 13 258 14 20 8 30 6 87 326 ...
## $ : int [1:431] 1 4 2019 9 149 16 35 221 22 585 ...
## $ : int [1:147] 1 146 242 31 7 4 1126 2406 2266 451 ...
## $ : int [1:684] 1 1810 8 516 7732 93 6 227 7 6 ...
## $ : int [1:383] 1 1028 11 86 8213 14 1327 1210 1124 5205 ...
## $ : int [1:324] 1 2 8810 322 7398 5 68 1667 476 2 ...
## $ : int [1:252] 1 13 286 1017 76 5 8 30 1202 13 ...
## $ : int [1:263] 1 48 335 6 337 7 22 1359 5 104 ...
## $ : int [1:787] 1 6 1380 6733 3453 54 49 432 7 5682 ...
## $ : int [1:211] 1 14 20 218 290 4 22 12 16 3551 ...
## $ : int [1:314] 1 49 24 38 2 1028 1404 10 10 138 ...
## $ : int [1:118] 1 480 302 18 6 20 7 14 58 6 ...
## $ : int [1:390] 1 670 5304 1616 97 6 20 40 14 21 ...
## $ : int [1:132] 1 1756 5663 9 2990 2 133 177 17 6 ...
## $ : int [1:710] 1 1065 2474 7 3508 2 645 113 17 6 ...
## $ : int [1:306] 1 17 210 14 9 35 6213 431 7 4 ...
## $ : int [1:167] 1 2500 1040 4 327 1208 44 14 215 28 ...
## $ : int [1:115] 1 11 4 402 3469 111 7 178 37 69 ...
## $ : int [1:95] 1 435 8 67 14 17 72 5 61 761 ...
## $ : int [1:158] 1 31 7 61 118 369 839 14 20 120 ...
## $ : int [1:156] 1 66 371 2 2 373 21 284 2 2567 ...
## $ : int [1:82] 1 4 1126 282 13 69 8 67 14 20 ...
## $ : int [1:502] 1 14 22 7930 236 314 33 2 5510 750 ...
## $ : int [1:314] 1 13 144 1260 138 13 520 14 418 7 ...
## $ : int [1:190] 1 13 92 400 140 46 7 61 96 8 ...
## $ : int [1:174] 1 61 795 203 30 6 227 7 6 1361 ...
## $ : int [1:60] 1 18 6 20 19 6 114 40 14 13 ...
## $ : int [1:145] 1 13 219 14 22 5236 145 137 780 23 ...
## $ : int [1:214] 1 11 192 5192 2 125 2139 1253 7 2 ...
## $ : int [1:659] 1 541 5156 517 19 4 4791 7 2408 827 ...
## $ : int [1:408] 1 474 66 66 473 8 67 14 20 5 ...
## $ : int [1:515] 1 7931 4 425 410 2568 4 876 7 4 ...
## $ : int [1:461] 1 121 81 13 895 13 473 8 358 14 ...
## $ : int [1:202] 1 13 66 215 28 1059 6 275 22 39 ...
## $ : int [1:238] 1 827 2 2 10 10 1251 8598 300 2 ...
## $ : int [1:170] 1 24 15 76 183 593 11 14 20 21 ...
## $ : int [1:107] 1 14 20 9 389 10 10 13 16 2 ...
## [list output truncated]
str(train_data[[1]])
str(train_labels)## int [1:25000] 1 0 0 1 0 0 1 0 1 0 ...
train_labels[[1]]
Since we restricted ourselves to the top 10,000 most frequent words,
max(sapply(train_data, max))## [1] 9999
max(sapply(train_data, max))
For kicks,
word_index <- dataset_imdb_word_index()
reverse_word_index <- names(word_index)
names(reverse_word_index) <- as.character(word_index)
decoded_words <- train_data[[1]] %>%
sapply(function(i) {
if (i > 3)
reverse_word_index[[as.character(i - 3)]]
else
"?"
})
decoded_review <- paste0(decoded_words, collapse = " ")# word_index is a dictionary mapping words to an integer index
word_index <- dataset_imdb_word_index()
# We reverse it, mapping integer indices to words
reverse_word_index <- names(word_index)
names(reverse_word_index) <- word_index
# We decode the review; note that our indices were offset by 3
# because 0, 1 and 2 are reserved indices for "padding", "start of sequence", and "unknown".
decoded_review <- sapply(train_data[[1]], function(index) {
word <-
if (index >= 3)
reverse_word_index[[as.character(index - 3)]]
if (!is.null(word))
word
else
"?"
})
decoded_review## [1] "? this film was just brilliant casting location scenery story direction everyone's really suited the part they played and you could just imagine being there robert ? is an amazing actor and now the same being director ? father came from the same scottish island as myself so i loved the fact there was a real connection with this film the witty remarks throughout the film were great it was just brilliant so much that i bought the film as soon as it was released for ? and would recommend it to everyone to watch and the fly fishing was amazing really cried at the end it was so sad and you know what they say if you cry at a film it must have been good and this definitely was also ? to the two little boy's that played the ? of norman and paul they were just brilliant children are often left out of the ? list i think because the stars that play them all grown up are such a big profile for the whole film but these children are amazing and should be praised for what they have done don't you think the whole story was so lovely because it was true and was someone's life after all that was shared with us all"
cat(decoded_review)
You can’t feed lists of integers into a neural network.
There are two ways to do that:
(samples, word_indices),[3, 5]
Let’s go with the latter solution
vectorize_sequences <- function(sequences, dimension = 10000) {
# Create an all-zero matrix of shape (len(sequences), dimension)
results <- array(0, dim = c(length(sequences), dimension))
for (i in seq_along(sequences)) {
# Sets specific indices of results[i] to 1s
sequence <- sequences[[i]]
for (j in sequence)
results[i, j] <- 1
}
results
}# Our vectorized training data
x_train <- vectorize_sequences(train_data)# Our vectorized test data
x_test <- vectorize_sequences(test_data)vectorize_sequences <- function(sequences, dimension = 10000) {
# Create an all-zero matrix of shape (len(sequences), dimension)
results <- matrix(0, nrow = length(sequences), ncol = dimension)
for (i in 1:length(sequences))
# Sets specific indices of results[i] to 1s
results[i, sequences[[i]]] <- 1
results
}
# Our vectorized training data
x_train <- vectorize_sequences(train_data)
# Our vectorized test data
x_test <- vectorize_sequences(test_data)
Here’s what our samples look like now:
str(x_train)## num [1:25000, 1:10000] 1 1 1 1 1 1 1 1 1 1 ...
str(x_train[1,])
We should also vectorize our labels,
# Our vectorized labels
y_train <- as.numeric(train_labels)
y_test <- as.numeric(test_labels)# Our vectorized labels
y_train <- as.numeric(train_labels)
y_test <- as.numeric(test_labels)
Now our data is ready to be fed into a neural network.
Our input data is vectors, and the labels are scalars (1s and 0s):
layer_dense(units = 16, activation = "relu").The argument being passed to each dense layer (16)
output = relu(dot(W, input) + b)Having 16 hidden units means that the weight matrix
W
(input_dimension, 16),W will project the input data
b and apply the
relu operation). You can intuitively understand the
dimensionality of your representation spaceFor the time being, you will have to trust us
relu as their
“activation function”,relu (rectified linear unit)
[0, 1] interval,
3-layer network
And here’s the Keras implementation,
model <- keras_model_sequential() %>%
layer_dense(16, activation = "relu") %>%
layer_dense(16, activation = "relu") %>%
layer_dense(1, activation = "sigmoid")library(keras)
model <- keras_model_sequential() %>%
layer_dense(units = 16,
activation = "relu",
input_shape = c(10000)) %>%
layer_dense(units = 16, activation = "relu") %>%
layer_dense(units = 1, activation = "sigmoid")
Since we are facing a binary classification problem
binary_crossentropy loss.mean_squared_error.Here’s the step where we configure our model
rmsprop optimizerbinary_crossentropy loss function.Note that we will also monitor accuracy during training.
model %>% compile(optimizer = "rmsprop",
loss = "binary_crossentropy",
metrics = "accuracy")model %>% compile(optimizer = "rmsprop",
loss = "binary_crossentropy",
metrics = c("accuracy"))
You’re passing your optimizer, loss function, and metrics as strings,
rmsprop,
binary_crossentropy, and accuracy
optimizer
argument:Here is an example of reducing the learning rate lr
model %>% compile(
optimizer = optimizer_rmsprop(lr = 0.001),
loss = "binary_crossentropy",
metrics = c("accuracy")
)
The latter can be done by
loss or metrics arguments:model %>% compile(optimizer = optimizer_rmsprop(lr = 0.001),
loss = loss_binary_crossentropy,
metrics = metric_binary_accuracy)
In order to monitor during training
x_val <- x_train[seq(10000),]
partial_x_train <- x_train[-seq(10000),]
y_val <- y_train[seq(10000)]
partial_y_train <- y_train[-seq(10000)]val_indices <- 1:10000
x_val <- x_train[val_indices, ]
partial_x_train <- x_train[-val_indices, ]
y_val <- y_train[val_indices]
partial_y_train <- y_train[-val_indices]
# ```{r, echo=TRUE, results='hide'}
model %>% compile(optimizer = "rmsprop",
loss = "binary_crossentropy",
metrics = c("accuracy"))
x_train and
y_train tensors),
validation_data argument:history <- model %>% fit(
partial_x_train,
partial_y_train,
epochs = 20,
batch_size = 512,
validation_data = list(x_val, y_val)
)history <- model %>% fit(
partial_x_train,
partial_y_train,
epochs = 20,
batch_size = 512,
validation_data = list(x_val, y_val)
)
Note that the call to fit() returns a
history object.
str(history$metrics)## List of 4
## $ loss : num [1:20] 0.564 0.356 0.268 0.216 0.182 ...
## $ accuracy : num [1:20] 0.75 0.89 0.916 0.93 0.94 ...
## $ val_loss : num [1:20] 0.435 0.338 0.3 0.293 0.282 ...
## $ val_accuracy: num [1:20] 0.858 0.876 0.884 0.882 0.886 ...
str(history)
history object includeshistory$params)history$metrics).The history object
plot() method that enables usplot(history)plot(history)
history_df <- as.data.frame(history)
str(history_df)## 'data.frame': 80 obs. of 4 variables:
## $ epoch : int 1 2 3 4 5 6 7 8 9 10 ...
## $ value : num 0.564 0.356 0.268 0.216 0.182 ...
## $ metric: Factor w/ 2 levels "loss","accuracy": 1 1 1 1 1 1 1 1 1 1 ...
## $ data : Factor w/ 2 levels "training","validation": 1 1 1 1 1 1 1 1 1 1 ...
The accuracy is plotted on the bottom panel
Note that your own results may vary slightly
The dots are the training loss and accuracy,
Note that your own results may vary slightly
As you can see,
That’s what you would expect when running a gradient-descent optimization
In this case, to prevent overfitting,
model <- keras_model_sequential() %>%
layer_dense(16, activation = "relu") %>%
layer_dense(16, activation = "relu") %>%
layer_dense(1, activation = "sigmoid")
model %>% compile(optimizer = "rmsprop",
loss = "binary_crossentropy",
metrics = "accuracy")
model %>% fit(x_train, y_train, epochs = 4, batch_size = 512)
results <- model %>% evaluate(x_test, y_test)# ```{r, echo=TRUE, results='hide'}
model <- keras_model_sequential() %>%
layer_dense(units = 16,
activation = "relu",
input_shape = c(10000)) %>%
layer_dense(units = 16, activation = "relu") %>%
layer_dense(units = 1, activation = "sigmoid")
model %>% compile(optimizer = "rmsprop",
loss = "binary_crossentropy",
metrics = c("accuracy"))
model %>% fit(x_train, y_train, epochs = 4, batch_size = 512)
results <- model %>% evaluate(x_test, y_test)
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glimpse(results)## Named num [1:2] 0.297 0.88
## - attr(*, "names")= chr [1:2] "loss" "accuracy"
results
With state-of-the-art approaches,
After having trained a network,
predict method:## [,1]
## [1,] 1.809323e-01
## [2,] 9.995760e-01
## [3,] 5.644663e-01
## [4,] 7.213696e-01
## [5,] 9.194620e-01
## [6,] 6.935150e-01
## [7,] 9.976543e-01
## [8,] 7.234948e-03
## [9,] 9.577290e-01
## [10,] 9.708132e-01
## [11,] 8.362126e-01
## [12,] 6.386790e-03
## [13,] 1.489181e-04
## [14,] 1.815337e-02
## [15,] 9.927796e-01
## [16,] 1.730158e-04
## [17,] 9.071934e-01
## [18,] 4.735232e-01
## [19,] 4.328170e-03
## [20,] 4.784987e-02
## [21,] 9.950227e-01
## [22,] 9.919990e-01
## [23,] 2.480482e-01
## [24,] 9.167549e-01
## [25,] 7.412857e-01
## [26,] 9.200405e-01
## [27,] 2.976402e-02
## [28,] 9.044346e-01
## [29,] 9.465023e-01
## [30,] 2.464158e-04
## [31,] 9.706364e-01
## [32,] 1.398314e-01
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## [34,] 5.860220e-06
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## [41,] 9.681451e-01
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## [47,] 3.169743e-02
## [48,] 7.066271e-04
## [49,] 1.031139e-02
## [50,] 2.579865e-01
## [51,] 3.586534e-03
## [52,] 2.287266e-01
## [53,] 7.119795e-01
## [54,] 8.712035e-01
## [55,] 8.180949e-01
## [56,] 1.252218e-01
## [57,] 5.272564e-01
## [58,] 7.468358e-01
## [59,] 3.089978e-03
## [60,] 5.150989e-01
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## [62,] 9.598553e-02
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## [64,] 2.096784e-02
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## [66,] 9.980721e-01
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## [88,] 8.392849e-01
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## [90,] 6.785294e-01
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## [93,] 3.968510e-02
## [94,] 9.945129e-01
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## [24708,] 1.309612e-02
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## [24710,] 9.999294e-01
## [24711,] 3.708305e-03
## [24712,] 1.640549e-03
## [24713,] 9.609080e-04
## [24714,] 2.730562e-02
## [24715,] 1.476519e-01
## [24716,] 5.195658e-01
## [24717,] 3.081245e-01
## [24718,] 8.770389e-01
## [24719,] 4.951018e-03
## [24720,] 3.374170e-04
## [24721,] 9.999740e-01
## [24722,] 3.285906e-01
## [24723,] 7.029824e-05
## [24724,] 9.987535e-01
## [24725,] 5.294270e-03
## [24726,] 9.999703e-01
## [24727,] 8.976293e-06
## [24728,] 8.762866e-01
## [24729,] 9.965591e-01
## [24730,] 3.127650e-02
## [24731,] 1.430948e-03
## [24732,] 1.822199e-03
## [24733,] 6.614048e-03
## [24734,] 7.572549e-01
## [24735,] 1.561689e-01
## [24736,] 4.130038e-01
## [24737,] 9.355690e-01
## [24738,] 9.122405e-01
## [24739,] 6.081845e-01
## [24740,] 9.997289e-01
## [24741,] 9.981403e-01
## [24742,] 3.290071e-04
## [24743,] 9.996756e-01
## [24744,] 9.943093e-01
## [24745,] 5.111856e-01
## [24746,] 8.355756e-01
## [24747,] 8.675184e-04
## [24748,] 1.076496e-02
## [24749,] 5.045503e-02
## [24750,] 9.251677e-01
## [24751,] 5.344767e-02
## [24752,] 1.151058e-01
## [24753,] 9.592047e-01
## [24754,] 9.555561e-01
## [24755,] 1.115303e-02
## [24756,] 2.253168e-02
## [24757,] 1.358609e-02
## [24758,] 9.966138e-01
## [24759,] 9.592680e-01
## [24760,] 1.946197e-03
## [24761,] 2.197413e-03
## [24762,] 8.820298e-01
## [24763,] 9.966316e-01
## [24764,] 8.003181e-01
## [24765,] 5.346307e-01
## [24766,] 4.464657e-03
## [24767,] 7.919754e-03
## [24768,] 2.518820e-01
## [24769,] 6.938896e-01
## [24770,] 3.479838e-01
## [24771,] 7.690099e-01
## [24772,] 8.353176e-01
## [24773,] 9.824159e-01
## [24774,] 1.621479e-01
## [24775,] 3.957547e-02
## [24776,] 9.908895e-01
## [24777,] 9.984996e-01
## [24778,] 2.327600e-01
## [24779,] 2.667120e-03
## [24780,] 8.214360e-02
## [24781,] 1.764934e-02
## [24782,] 8.657869e-03
## [24783,] 8.424096e-01
## [24784,] 1.250031e-01
## [24785,] 1.559761e-03
## [24786,] 3.534236e-05
## [24787,] 1.268524e-04
## [24788,] 9.295498e-01
## [24789,] 6.573298e-03
## [24790,] 1.809806e-02
## [24791,] 8.512504e-01
## [24792,] 7.637516e-01
## [24793,] 9.930910e-01
## [24794,] 7.682682e-01
## [24795,] 4.565500e-01
## [24796,] 9.955100e-01
## [24797,] 1.357750e-01
## [24798,] 2.852435e-01
## [24799,] 1.560921e-01
## [24800,] 2.005600e-03
## [24801,] 5.385218e-02
## [24802,] 4.161819e-03
## [24803,] 8.719821e-01
## [24804,] 9.860895e-01
## [24805,] 5.373286e-06
## [24806,] 5.521966e-01
## [24807,] 6.292091e-01
## [24808,] 1.791318e-02
## [24809,] 8.759705e-01
## [24810,] 2.021309e-02
## [24811,] 1.264515e-01
## [24812,] 6.165643e-03
## [24813,] 6.518010e-01
## [24814,] 5.639805e-02
## [24815,] 5.188947e-01
## [24816,] 9.626456e-01
## [24817,] 1.679293e-01
## [24818,] 9.906137e-01
## [24819,] 3.389786e-01
## [24820,] 2.812696e-02
## [24821,] 1.741720e-02
## [24822,] 9.390001e-01
## [24823,] 1.300966e-02
## [24824,] 1.231894e-02
## [24825,] 6.428911e-02
## [24826,] 8.809685e-01
## [24827,] 7.909036e-01
## [24828,] 5.836832e-02
## [24829,] 9.246130e-01
## [24830,] 2.102110e-03
## [24831,] 5.196188e-02
## [24832,] 9.020481e-02
## [24833,] 1.991838e-03
## [24834,] 9.925183e-01
## [24835,] 6.026426e-02
## [24836,] 9.989079e-01
## [24837,] 6.845502e-01
## [24838,] 4.905607e-01
## [24839,] 9.832087e-01
## [24840,] 9.900144e-01
## [24841,] 7.789637e-05
## [24842,] 8.450133e-02
## [24843,] 9.063631e-01
## [24844,] 3.670092e-02
## [24845,] 1.998778e-02
## [24846,] 8.629155e-01
## [24847,] 8.769152e-01
## [24848,] 1.277260e-01
## [24849,] 9.718027e-01
## [24850,] 9.718598e-01
## [24851,] 7.734422e-03
## [24852,] 1.216102e-02
## [24853,] 7.641162e-01
## [24854,] 4.675112e-03
## [24855,] 4.889610e-01
## [24856,] 6.248385e-01
## [24857,] 5.383789e-03
## [24858,] 2.675319e-01
## [24859,] 2.330573e-05
## [24860,] 9.296845e-01
## [24861,] 4.471177e-01
## [24862,] 8.755432e-01
## [24863,] 2.726047e-01
## [24864,] 4.574155e-03
## [24865,] 8.201724e-01
## [24866,] 1.951344e-02
## [24867,] 6.756607e-02
## [24868,] 8.047127e-01
## [24869,] 9.412595e-01
## [24870,] 7.719343e-01
## [24871,] 7.038699e-01
## [24872,] 8.919522e-02
## [24873,] 3.379346e-01
## [24874,] 5.591932e-01
## [24875,] 7.739745e-03
## [24876,] 9.994985e-01
## [24877,] 9.569312e-01
## [24878,] 8.726880e-02
## [24879,] 8.079720e-01
## [24880,] 1.737255e-01
## [24881,] 3.129116e-05
## [24882,] 1.182594e-03
## [24883,] 6.712236e-01
## [24884,] 4.761741e-02
## [24885,] 1.263323e-01
## [24886,] 9.565090e-01
## [24887,] 2.435417e-01
## [24888,] 1.131691e-02
## [24889,] 9.915863e-01
## [24890,] 1.478861e-01
## [24891,] 9.823903e-01
## [24892,] 6.510865e-01
## [24893,] 9.395406e-01
## [24894,] 7.526447e-01
## [24895,] 8.403794e-03
## [24896,] 8.151969e-01
## [24897,] 1.746117e-03
## [24898,] 2.412618e-04
## [24899,] 2.244237e-02
## [24900,] 9.355348e-01
## [24901,] 9.536199e-01
## [24902,] 1.627520e-01
## [24903,] 2.204280e-03
## [24904,] 2.712900e-03
## [24905,] 6.765408e-03
## [24906,] 9.993649e-01
## [24907,] 9.838021e-01
## [24908,] 1.164848e-03
## [24909,] 9.774272e-01
## [24910,] 1.539741e-01
## [24911,] 2.136132e-01
## [24912,] 7.221838e-05
## [24913,] 5.100614e-03
## [24914,] 3.384619e-03
## [24915,] 9.619740e-01
## [24916,] 2.633864e-02
## [24917,] 8.624977e-01
## [24918,] 6.356140e-02
## [24919,] 9.645644e-01
## [24920,] 8.817286e-01
## [24921,] 4.695052e-01
## [24922,] 3.372674e-02
## [24923,] 9.998477e-01
## [24924,] 6.261634e-02
## [24925,] 7.205223e-02
## [24926,] 1.380065e-02
## [24927,] 6.337003e-01
## [24928,] 6.172195e-02
## [24929,] 5.139667e-03
## [24930,] 3.453147e-01
## [24931,] 6.248859e-02
## [24932,] 9.808352e-01
## [24933,] 9.060351e-01
## [24934,] 6.590093e-03
## [24935,] 9.874194e-01
## [24936,] 9.859599e-01
## [24937,] 3.036077e-01
## [24938,] 3.147335e-02
## [24939,] 4.322355e-02
## [24940,] 9.660822e-01
## [24941,] 9.593841e-01
## [24942,] 9.178557e-01
## [24943,] 6.986324e-01
## [24944,] 4.669711e-02
## [24945,] 9.896827e-01
## [24946,] 2.755826e-03
## [24947,] 1.309591e-01
## [24948,] 3.828813e-03
## [24949,] 2.656065e-02
## [24950,] 1.732427e-01
## [24951,] 8.113167e-01
## [24952,] 8.724517e-07
## [24953,] 1.262761e-06
## [24954,] 7.182690e-01
## [24955,] 1.210095e-01
## [24956,] 9.999441e-01
## [24957,] 6.794735e-03
## [24958,] 1.760919e-01
## [24959,] 1.250728e-02
## [24960,] 7.475549e-02
## [24961,] 1.444033e-02
## [24962,] 9.228146e-01
## [24963,] 1.383160e-01
## [24964,] 4.136506e-02
## [24965,] 8.014644e-04
## [24966,] 9.961369e-03
## [24967,] 3.663588e-01
## [24968,] 9.460790e-01
## [24969,] 7.004834e-01
## [24970,] 6.017078e-01
## [24971,] 9.941562e-01
## [24972,] 6.928720e-03
## [24973,] 8.979579e-03
## [24974,] 9.614748e-01
## [24975,] 9.489493e-01
## [24976,] 4.653215e-01
## [24977,] 3.306066e-03
## [24978,] 9.751461e-01
## [24979,] 5.848497e-01
## [24980,] 3.631917e-01
## [24981,] 9.019862e-01
## [24982,] 9.766631e-01
## [24983,] 9.695361e-01
## [24984,] 3.587396e-03
## [24985,] 5.377835e-01
## [24986,] 2.998480e-01
## [24987,] 9.924567e-01
## [24988,] 1.068753e-03
## [24989,] 9.328419e-01
## [24990,] 4.176937e-01
## [24991,] 6.621515e-01
## [24992,] 4.278349e-04
## [24993,] 9.964071e-01
## [24994,] 3.808199e-01
## [24995,] 9.620006e-01
## [24996,] 9.972059e-01
## [24997,] 4.791435e-01
## [24998,] 8.716574e-02
## [24999,] 7.349376e-02
## [25000,] 4.632613e-01
model %>% predict(x_test[1:10, ])
As you can see, the network is very confident for some samples
mse loss function
binary_crossentropy.tanh activation
relu.These experiments will help convince you
Here’s what you should take away from this example:
relu activations
sigmoid activation.binary_crossentropy.rmsprop optimizer is generally a good enough
choice,
[1] Francois Chollet, J. J. Allaire, Deep Learning with R, https://www.manning.com/books/deep-learning-with-r Manning Publications, 2018.